Classical reversible logic and quantum computing share the common feature that all computations are reversible, each result of a computation can be brought back to the initial state without loss of information.
Reversible logic was originally proposed as a way to build classical computers with very low energy requirements. Its greatest impact so far has in fact been on the field of quantum computing, where it is used pervasively -- but for an entirely different purpose. Quantum interference effects offer the potential for speeding up certain classical calculations. But if state information is expelled from a quantum computer into the unmodeled environment -- as happens whenever an irreversible operation is performed -- then it becomes impossible to predict or control when interference will occur. Reversibility is necessary because it allows bits to be erased by uncomputing them rather than simply expelling them, preserving control over interference effects.
In the last chapter, we saw that it is theoretically possible to switch a logically reversible gate without dissipating any energy at all (recall the proof of the Landauer-Shannon result). If there is no dissipation, then no information is ever being discarded; therefore, if we know the state of the system completely at any instant of time, we should be able to infer its state at any previous instant. This is consistent with the equations of quantum mechanics (e.g., the Schro¨dinger equation, or the Pauli equation) which are reversible in time. This property of quantum mechanical systems, known as “time reversal symmetry”, guarantees that if we know the state of a system at a time t0, we can tell what the state was at any time t < t0. Because of this fundamental connection between physical reversibility, logical reversibility, and the equations of quantum mechanics, we would expect logically reversible gates to behave as non-classical (quantum mechanical) computing machinery.∗ This will bring us to the topic of quantum computing and quantum logic gates, but before we get there, let us explore reversible logic in a little more detail.
In the last chapter, we saw that it is theoretically possible to switch a logically reversible gate without dissipating any energy at all (recall the proof of the Landauer-Shannon result). If there is no dissipation, then no information is ever being discarded; therefore, if we know the state of the system completely at any instant of time, we should be able to infer its state at any previous instant. This is consistent with the equations of quantum mechanics (e.g., the Schro¨dinger equation, or the Pauli Equation) which are reversible in time. This property of quantum mechanical systems, known as ‘time reversal symmetry’, guarantees that if we know the state of a system at a time t0, we can tell what the state was at any time t < t0. Because of this fundamental connection between physical reversibility, logical reversibility, and the equations of quantum mechanics, we would expect logically reversible gates to behave as non-classical (quantum mechanical) computing machinery∗. This will bring us to the topic of quantum computing and quantum logic gates, but before we get there, let us explore reversible logic in a little more detail.
This work presents the logical reversibility. The inputs and outputs of reversible logic gates can be uniquely retrievable from each other. The reversible logic operations can't erase information and dissipate zero heat. The circuit actually operates in a backward operation, allows reproducing the inputs from the outputs and consumes zero power. As the basic elements of any logic circuit, logic gates are used to realize Boolean functions. By combining reversible logic gates, reversible circuits can perform complex logical and arithmetic operations. A one-to-one mapping between inputs and outputs is realized. The logical operations run backwards by cascading a reversible logic gate with its dual (inverse). Reversible circuits are also called lossless circuits, as there is neither energy loss nor information loss. These circuits are very attractive for applications where extremely low power consumption, or heat dissipation, is desirable in areas ranging from communications, low power VLSI (very large-scale integration) technology, optical computing to nanotechnology. Reversible logic found to be very useful in quantum computing where the quantum evolution is inherently reversible.
It has been realized that quantum computing is one of the latest technologies using reversible logic. It is observed that increasing growth of transistor density, power consumption will reach their limits in conventional technologies. In conventional Circuits during the logic operations bits of information is erased resulting dissipation of energy in significant amount. Thus, if Circuits are designed so that information bits can be preserved, the power use can be reduced. In case of reversible logic computation, the information bits are not lost. We can use reversible logic technology for minimizing the power consumption, heat dissipation, increasing speed etc. This paper describes various logic gates based on reversible logic like Toffoli, Peres, Fredkin, and Feynman etc. A comparative between classical and quantum logic gates is also given on various parameters along with limitations of conventional computing.
Reversible computing provides a foundational framework for understanding quantum computation.This paper first examines classical reversible logic gates, including the CNOT and Toffoli gates, and demonstrates how they can simulate arbitrary Boolean functions.We then extend these concepts to quantum gates and circuits, where all operations are inherently unitary and reversible.Quantum algorithms such as the Deutsch-Jozsa algorithm, phase estimation, and Shor's factoring algorithm are discussed to illustrate how reversibility enables exponential computational speedups.Finally, current challenges and future directions in quantum hardware and algorithm design are presented.Highlighting the essential role of reversible computing in the realisation of practical quantum computers.